Federated learning (FL) enables collaborative model training without centralizing data. However, the traditional FL framework is cloud-based and suffers from high communication latency. On the other hand, the edge-based FL framework that relies on an edge server co-located with access point for model aggregation has low communication latency but suffers from degraded model accuracy due to the limited coverage of edge server. In light of high-accuracy but high-latency cloud-based FL and low-latency but low-accuracy edge-based FL, this paper proposes a new FL framework based on cooperative mobile edge networking called cooperative federated edge learning (CFEL) to enable both high-accuracy and low-latency distributed intelligence at mobile edge networks. Considering the unique two-tier network architecture of CFEL, a novel federated optimization method dubbed cooperative edge-based federated averaging (CE-FedAvg) is further developed, wherein each edge server both coordinates collaborative model training among the devices within its own coverage and cooperates with other edge servers to learn a shared global model through decentralized consensus. Experimental results based on benchmark datasets show that CFEL can largely speed up the convergence speed and reduce the training time to achieve a target model accuracy compared with prior FL frameworks.